Introduction to numerical analysis

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Introduction to numerical analysis / Arnold Neumaier

資料種別:: 電子ブック
形態:: 1 online resource (viii, 356 p.)
著者名:: Neumaier, A.
ISBN:: 9780511612916 [0511612915] (: electronic bk)
書誌ID:: EB00000370

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注記:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

主題:

Numerical analysis

言語:

英語

目次情報:

The numerical evaluation of expressions / 1：

Linear systems of equations / 2：

Interpolation and numerical differentiation / 3：

Numerical integration / 4：

Univariate nonlinear equations / 5：

Systems of nonlinear equations / 6：

Preface

The Numerical Evaluation of Expressions / 1.：

Arithmetic Expressions and Automatic Differentiation / 1.1：

Numbers, Operations, and Elementary Functions / 1.2：

Numerical Stability / 1.3：

Error Propagation and Condition / 1.4：

Interval Arithmetic / 1.5：

Exercises / 1.6：

Linear Systems of Equations / 2.：

Gaussian Elimination / 2.1：

Variations on a Theme / 2.2：

Rounding Errors, Equilibration, and Pivot Search / 2.3：

Vector and Matrix Norms / 2.4：

Condition Numbers and Data Perturbations / 2.5：

Iterative Refinement / 2.6：

Error Bounds for Solutions of Linear Systems / 2.7：

Interpolation and Numerical Differentiation / 2.8：

Interpolation by Polynomials / 3.1：

Extrapolation and Numerical Differentiation / 3.2：

Cubic Splines / 3.3：

Approximation by Splines / 3.4：

Radial Basis Functions / 3.5：

Numerical Integration / 3.6：

The Accuracy of Quadrature Formulas / 4.1：

Gaussian Quadrature Formulas / 4.2：

The Trapezoidal Rule / 4.3：

Adaptive Integration / 4.4：

Solving Ordinary Differential Equations / 4.5：

Step Size and Order Control / 4.6：

Univariate Nonlinear Equations / 4.7：

The Secant Method / 5.1：

Bisection Methods / 5.2：

Spectral Bisection Methods for Eigenvalues / 5.3：

Convergence Order / 5.4：

Error Analysis / 5.5：

Complex Zeros / 5.6：

Methods Using Derivative Information / 5.7：

Systems of Nonlinear Equations / 5.8：

Preliminaries / 6.1：

Newton's Method and Its Variants / 6.2：

Further Techniques for Nonlinear Systems / 6.3：

References / 6.5：

Index

The numerical evaluation of expressions / 1：

Linear systems of equations / 2：

Interpolation and numerical differentiation / 3：

Numerical integration / 4：

Univariate nonlinear equations / 5：

Systems of nonlinear equations / 6：

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